Biomedical Imaging. X ray imaging. Patrícia Figueiredo IST

Transcription

1 Biomedical Imaging X ray imaging Patrícia Figueiredo IST

2 Overview Production of X rays Interaction of electrons with matter X ray spectrum X ray tube Interaction of X rays with matter Photoelectric effects and Compton effect X ray attenuation X ray dosimetry

3 X rays - X rays are beams of high energy photons, with wavelengths ~ m. - Because of their high penetration power, they are used in the analysis of the structure of different materials, either through X ray diffraction (crystallography) or X ray transmission (medical radiography and computed tomography).

4 Production of X rays X rays are produced through the acceleration of an electron beam from a cathode where they are emitted towards an anode where they interact with a target. Accelerating voltage: ΔV p ~15 150kV, I~ mA Heating through passage of electric current Thermionic emission of electrons Acceleration of free electrons towards the anode X ray emission through interaction of free electrons with the target

5 Interactions of electrons with matter Atomic excitation: Ionization: Joule effect: Heating!

6 Interactions of electrons with matter Bremsstrahlung (braking radiation) Maximum X ray energy E max = E 1 E 2 = 0 hν = E 1 = E max ΔE max kvp Continuous range of energies

7 X ray spectrum Bremsstrahlung Relative nb photons Efficiency of Bremsstrahlung radiation: η kvpz Maximum energy E kvp max Photon energy [kev]

8 Interactions of electrons with matter Ionization: characteristic radiation e - E e =E inc -E 0 e - E o X E inc Eo E 1 E 1 -E 0 e - E 2 e - E o X E 2 -E 0 E = Δ i E i Atomic level transitions: discrete enery levels

9 Interactions of electrons with matter Ionization: characteristic radiation E=20-2.6=17.4 ev E=69-11=58 ev e - E o X E 1 E 1 -E 0 E 2 e - E o X E= =19.61 ev E=69-2.3=66.7 ev E 2 -E 0

10 X ray spectrum Bremsstrahlung Internal filtering Characteristic radiation E kvp max Maximum energy [kev]

11 X ray tube High melting point targets (anodes) Rotating anodes (~3000 rpm) Focusing tube (cathods) Beveled targets (angles 5-20 ) Target Z Melting point W C Mo C 1B2YA High Voltage Rectifier Tubes. Tube on left is manufactured by Sylvania, the right tube is General Electric manufactured. Tubes show glass discoloration (browning) from X- ray production.

12 X ray tube Effective focal spot size: f = F sinθ Range = 2 D tanθ (θ ~ 5-20 f ~ mm) Effective focal spot size F θ D f Range Focal spot size

13 X ray tube Main characteristics: - Tube voltage (accelerating voltage): kvp ~ kv, ~50 kv for mammography, ~130 kv in torax radiography -Tube current: ma ~ ma in radiography, ~1000 ma em CT, <50 ma in fluoroscopy - Output power: ma kvp [Watts] - Exposition time: [s] -Maximum power for an exposition of 0.1 s: kw P = 10 kw per 0.1 s: kvp = 80 kv ma = 125 ma - X ray beam intensity: I Z alvo ma (kvp) 2 [J m -2 ] - X ray maximum energy: E max = e kvp kvp [kev] - Focal spot size / Effective focal spot size: F / f [mm]

14 X ray tube Tube voltage [kvp]: Tube current [ma]: I (kvp) 2 E max kvp E peak shifted to higher energies Nb characteristic lines I ma E max unchanged E peak unchanged Nb characteristic lines unchanged

15 X ray tube Exposition time [s] / Maximum power in 0.1 s [kw]:

16 Interaction of X rays with matter Contrast between tissues in X-ray images arises from differential attenuation of the X-rays across the tissues. A certain fraction of X-rays pass straight through the body and undergo no interactions with the tissue: these X-rays are called primary radiation. X-rays can be scattered, an interaction that alters their trajectory between source and detector. They are called secondary radiation. X-rays, can be absorbed, they are called absorbed radiation.

17 Interaction of X rays with matter Photoelectric effect: absorption Absorbed Radiation Compton effect: inelastic diffusion Secondary radiation e - e - E 0 E 0 E 1 <<E 0 Valence shell An electron is ejected θ E 2 <<E 0 Pair production: annihilation E 1 <E 0 Coherent (Rayleigh): elastic diffusion Secondary radiation e - E 0 E 0 e + γ anhilation Incident radiation is converted in thermal vibration of the electrons there is no ionization Scattered angle increases θ E 1 <E 0

18 Interaction of X rays with matter Photoelectric effect: absorption p PE Z 3 /E 3

19 Interaction of X rays with matter Compton effect: inelastic diffusion p Compton ρn 0 The relatively small difference in energy between incident and scattered X-rays means that secondary radiation is detected with approximately the same efficiency as primary radiation.

20 Interaction of X rays with matter Compton effect: inelastic diffusion Distribuição de Compton: E X, scat = 1+ E X, inc E X, inc 2 mc ( 1 cosθ ) E X,inc [kev] θ E X,scat [kev]

21 X ray attenuation Photoelectric effect Compton Scattering e - e - E 0 E 1 <<E 0 E 2 <<E 0 E 0 θ E 1 <E 0 Incident X rays are absorbed and energy of secondary X rays is insufficient to reach detector X rays reaching the detector are: primary radiation, with preserved energy and direction. Depends on atomic number Z provides contrast betwen materials Incident X rays are scattered and energy of scattered X rays is sufficient to reach detector X rays reaching the detector are: secondary radiation with modified energy and direction. Does not depend on atomic number Z does not provide contrast betwen materials

22 X ray attenuation I 0 I 0 exp{-µ l Δx} ΔI = I 0 σn v Δx I(x ) = I 0 e σn v x = I 0 e µ l x CONTINUAR AQUI (IB-MTBiom) I 0 N 0 σ,n v,µ l Δx = intensity of incident X-rays = nb of incident photons : I 0 /2= I 0 exp{-σ N v HVL} HVL = ln 2 / µ l Half Value Layer σ [cm 2 ] = interaction cross section N v [cm -3 ] = nb of diffusing particles per unit volume of tissue µ l = σ N v [cm -1 ] = linear attenuation coefficient Interaction cross section: σ = σ Photoelectric + σ Compton + σ Rayleigh + σ PairProduction Linear attenuation coefficient: µ l = µ l (ρ, N 0, Z, E) [cm -1 ] Mass attenuation coefficient: µ = µ l / ρ µ = µ (N 0, Z, E) [cm 2 /g]

23 X ray attenuation Dependence on interaction cross section Mechanism Energy range E Z N 0 Elastic diffusion 1/E 2 Z 8/ kev Photoelectric effect 1/E 3 Z 3 N kev Compton diffusion Decreases with E - N MeV Pair production Increases with E Z 2 - > 5 MeV Operation region of X-rays used in medical diagnosis

24 X ray attenuation Energy dependence: In water I x = I 0 e µx µ = µ photoelectric + µ Compton + µ coherent The optimum X ray energy is ~ 30 kev (kvp ~ kv) where the photoelectric effect dominates.

25 X ray attenuation Energy dependence: Beam hardening: lower energy X rays suffer more attenuation, hence the mean energy of the X-ray beam increases as it goes through the tissues. Low Energy Δx [mm] If the X-rays have to pass through a large amount of tissue, such as in abdominal imaging, then beam hardening reduces image contrast by increasing the proportion of Comptonscattered X-rays due to the higher effective energy of the X-ray beam. High Energy - Affects HVL - Artifacts in CT

26 X ray attenuation Z

27 X ray attenuation Effective atomic number: Z eff = α iz i m i 1 m m = 3.8 Ex: Water (H 2 O)

28 X ray attenuation Material dependence (effective atomic number and electronic density): PE effect dominates (Z eff dependence) good contrast Compton effect dominates (ρn 0 dependence) bad contrast

29 X ray attenuation Material dependence (effective atomic number and electronic density): Factors that determine the attenuation coefficient of a material: - Effective atomic number: At lower energies, where the photoelectric effect dominates; The attenuation coefficient depends strongly on the X-ray energy. - Electronic density: At higher energies, where the Compton effect dominates; The attenuation coefficient does not depend much on the X-ray energy. Approximately:

30 X ray attenuation Material dependence: contrast agents K-edge better contrast Z I = 53 Z Ba = 56 Z Pb = 82 k-edge: 33.2 kev k-edge: 37.4 kev

31 Dosimetry Biological tissues Half-Value Layer for Muscle and Bone [cm] Material X-ray energy [kev] Bone Muscle The majority of X rays is absorbed by the tissues (>90%). X-ray tube materials

32 Dosimetry Dosimetric measures: Exposition X: [1 R = C/cm 3 = C/Kg ] Dose D: [1 Gy = 1 J/Kg ou 1 rad = 100 erg/g ] Factor f: f=d/x Equivalent dose: H E = ωi DiQF [Sv ou rem] 1 CT dose index: CTDI = T i + 7T 7T D z dz

33 Overview 1. X-ray image formation 2. Instrumentation 3. Image characteristics 4. Radiography techniques: angiography, fluoroscopy, mammography

34 Instrumentation X ray production: X ray tube / source X ray transmission: X ray attenuation X ray detection: X ray detectors

35 Instrumentation Image contrast should be optmized by minimizing the ratio between secondary (scattered) and primary radiation: CNR 1+ 1 I I scatt primary X ray source FOV X ray detector

36 Instrumentation Collimator restricts the FOV to the desired value ~10 30 cm CNR, dose X ray source FOV X ray detector collimator (Pb) Even with a collimator, scattered radiation can represent 50 90% of the detected radiation

37 Instrumentation Anti-scatter grid: absorbs significantly deflected photons ( CNR, dose) h Pb Bucky factor: F = t Exposure with grid Exposure without grid d Δ( CNR) = 1+ I inc scatt I inc primary 1+ I inc scatt I inc primary I trans scatt I trans primary X ray source X ray detector collimator (Pb) anti-scatter grid

38 Instrumentation Itensifying screen: phosphor excitation, X-rays visible light ( δ SNR, R) δ plastic base refelctive layer phosphor layer (Gd, La) protective layer film R=Resolution intensifying screen X ray source X ray detector collimator (Pb) anti-scatter grid

39 Instrumentation Conventional radiography: Photographic emulsion: darkening upon exposure photon intensity ( d SNR, R) Radiation detection ionization latent image Film exposure reduction of exposed silver salts to metallic silver film darkening Film blackening is quantified by a parameter known as Optical Density (OD) d Optical density latitude linear region Log exposure γ = OD loge 2 2 OD1 loge 1

40 Instrumentation Computed radiography: - Instead of a photographic emulsion, a cassette housing a plate of photostimulable phosphor is used. - Instead of film exposure, a laser scanner is used to read the cassette. Exposure to radiation phosphor excitation oxidation of Eu 2+ Laser absorption blue light emission upon deexcitation digitization

41 Instrumentation X ray detectors: X rays must be converted into radiation accessible to human vision Type of X ray detectors: - itensifying screen + photographic emulsion - cassette of photostimulable phosphor + laser scanner - scintillation detectors - crystals: NaI (Tl), CsI(Tl), BGO coupled to a photo-multiplier tube (PMT) or a photodiode array (e.g. TFT) - gas ionizing detectors: - ionizing chamber, proportional counter, Geiger-Muller counter Main characteristics of X ray detectors : - Sensitivity - Efficiency - Linearity - Energy resolution - Dead time

42 Instrumentation Digital radiography: - Scintillation crystal (CsI) matrix: crystal scintillation, X-rays visible light - Photodiodes in TFT array: visible light electric signal digital signal X rays crystal excitation electron-hole pairs electron-hole pairs collected at p-n junctions electrical current pre-amplifier

43 Image characteristics Geometric unsharpness (penumbra/blur, PSF) due to a finite size X ray source: Effective spot size: f [~ mm] Penumbra (PSF): Magnification factor: ( ) f S1 S0 P = = f (m 1) S0 S1 m = S 0 δ P f δ d 0 θ d 1 S 0 S 1

44 Image characteristics Measurement of the effective spot size PSF using a pinhole camera: S 1 S 0 ~75 µm f P = ( S S ) 1 S 0 0 f = S0 P S S 1 0

45 Image characteristics Measurement of the LSF using a grid of parallel lead septa: Measurement of the MTF using a line phantom: Using test objects:

46 Image characteristics Spatial resolution: R = R 2 spotsize + R 2 mag + R 2 screen + R 2 film effective focal spotsize f (tube) R ( S 1 -S 0, fixed S 0 R) magnification factor (patient-film-detectot distances) R ( S 0, fixed S 1 -S 0 R) screen thickness (diffusion distance) R film speed (size of silverparticles), or equivalent R

47 Image characteristics Signal to noise ratio (SNR) Main noise source in X ray imaging: - Quantum mottle: statistical variance of the distribution of X rays from the source Poisson distribution: p(n) = µ e N! N µ describes the number of occurences N of a random phenomenon per unit time and space, with mean µ and standard deviation For large N: µ µ N SNR = N σ σ = µ After attenuation by a material, X ray photons continue to follow Poisson statistics...

48 Image characteristics Signal to noise ratio (SNR) Factors affecting the SNR: - X ray tube voltage: kvp SNR - X ray tube current and exposure time: ma s SNR - X ray filtration: filtration SNR - Object size (thickness): object SNR N - Antiscatter grid ratio: h/d SNR - Intensifying screen thickness: δ SNR

49 Image characteristics Contrast to noise ratio (CNR) CNR depends on SNR and R. Other factors affecting the CNR: - X ray energy: E I scatt /I primary CNR - Object size (thickness): thickness I scatt /I primary CNR - Field-of-view (FOV ~10-30 cm): FOV I scatt CNR - Antiscatter grid ratio: h/d CNR

50 Radiography techniques Contrast agents Iodinated contrast agents are used to enhance contrast: K-edge - between vessels and surrounding tissues, by injection into the circulation; better contrast - between the gastro-intestinal tract (GI) and surrounding tissues, by oral administration.

51 Radiography techniques Angiography: imaging of blood vessels (by intra-venous or intra-arterial contrast injection) Conventional angiography vs Digital Subtraction Angiography (DSA): In this case, the subtraction of a precontrast image suppresses interfering structures from the 2D projection image so that the arteries become clearly defined (resolution ~100 µm). This image shows the pelvis of a patient that has had a kidney transplant and a stent placement.

52 Radiography techniques Fluoroscopy: continuous imaging (at very low energies ~25-30 kev) cine mode (cardiac and GI studies, stent and catheter placement, interventional radiology) Fluorescent image intensifier (CsI:Na) optimize SNR (in face of low energy)

53 Radiography techniques Mammography: imaging soft tissue with high resolution and CNR Low energies (~25-30 kev) - Mo target, high (and not low) energy filtering low energy to optimize CNR - Fast intensifying screen / film combinations to allow enough SNR at low energy - Large source to detector distance and small focal spot size high resolution (<1mm)

54 References Webb, Introduction to Biomedical Imaging, Wiley Cho, Foundations of Medical Imaging, Wiley Hendee, Medical Imaging Physics, Wiley 2002.